Boundary value problems to first-order complex partial differential equations in a ring domain

Vaitekhovich, Tatyana

doi:10.1080/10652460701736569

Cited by 37 publications

(26 citation statements)

References 6 publications

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“…Various kinds of boundary value problems for complex partial differential equations in different domains have been extensively investigated [1][2][3][4][5][6][7][8][9]14]. In particular, the authors studied harmonic boundary value problems in half disc and half ring [12].…”

Section: Schwarz Boundary Value Problemmentioning

confidence: 99%

Boundary value problems in a fan-shaped domain

Wang

2011

Advances in Pure and Applied Mathematics

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Section: Schwarz Boundary Value Problemmentioning

confidence: 99%

Boundary value problems in a fan-shaped domain

Wang

2011

Advances in Pure and Applied Mathematics

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“…One of the first result in this direction was obtained in [23] where a boundary value problem for a ring was solved. In the present paper, we combine methods applied to boundary value problems for complex partial differential equations in simply connected domains and for the Riemann-Hilbert type problems in multiply connected domains.…”

Section: Introductionmentioning

confidence: 96%

Schwarz problem for bi-analytic functions in multiply connected domains

Çelebi

Mityushev

2014

Complex Variables and Elliptic Equations

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The Schwarz problem for bi-analytic functions in unbounded circular multiply connected domains is considered. We combine constructive methods applied to boundary value problems for complex partial differential equations in simply connected domains and for the Riemann-Hilbert type problems in multiply connected domains. A general method is outlined and the case of doubly connected domains is discussed in details. Solution is obtained in the form of a series.

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“…In principle, our method is designed for real equations over real intervals. A possible generalization to complex domains is subject of future research, in connection with the problems (Schwarz, Dirichlet, Neumann and Robin) solved in [9].…”

Section: Introductionmentioning

confidence: 99%

The Liouville–Neumann expansion in one-dimensional boundary value problems

López

2010

Integral Transforms and Special Functions

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We consider boundary value problems of the formwith f , g and h continuous in [0, 1]. We use the Liouville-Neumann expansion to design a succession of functions y n (x) that converge uniformly on [0, 1] to the solution y(x) of that problem. In particular, when f (x), g(x) and h(x) are polynomials, y n (x) are also polynomials. We show that the Liouville-Neumann algorithm may be used to approximate eigenvalues and eigenfunctions of eigenvalue problems of the form y + f (x)y + [g(x) + λσ (x)]y = 0, x ∈ (0, 1), y(0) = y(1) = 0, with f , g and σ continuous in [0, 1]. It may be also used to approximate zeros of solutions of regular second-order linear differential equations and, in particular, of some special functions.

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Boundary value problems to first-order complex partial differential equations in a ring domain

Cited by 37 publications

References 6 publications

Boundary value problems in a fan-shaped domain

Boundary value problems in a fan-shaped domain

Schwarz problem for bi-analytic functions in multiply connected domains

The Liouville–Neumann expansion in one-dimensional boundary value problems

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